The \(\mathcal {A}_{1}\)  algorithm of Shah et al. [1]} is essentially a 1vr approach that uses Empirical Bernstein confidence bounds [2]}. Noting that it can just as well be implemented in a 1v1 form, we include such a variant, denoted \(\mathcal {A}_{1}\) -1v1, in our experimental comparisons with PPR. For good measure, we also include 1v1 and 1vr variants based on the KL-SN confidence bound [3]}, which finished second to PPR-Bernoulli for \(K = 2\)  (see Section ). Table REF  shows the performance of 1v1 and 1vr versions of PPR, \(\mathcal {A}_{1}\) , and KL-SN on a variety of distributions. We observe the same trend on each problem instance: (1) The 1v1 variant of each stopping rule outperforms the corresponding 1vr variant, and (2) PPR is most sample-efficient, followed by KL-SN and \(\mathcal {A}_{1}\) . In line with the upper bound from theorems REF  and REF , it does appear that the sample complexity is largely determined by \(p_{1}\)  and \(p_{2}\)  (identical for instances \(\mathcal {P}_{5}\)  and \(\mathcal {P}_{6}\) ) in the table. The logarithmic dependence on \(K\)  results in a slightly larger number of samples for all these methods on \(\mathcal {P}_{6}\) .
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